Chapter 3 – Elementary particles

Patricle spin

Spin is the strangest of the particle properties. All the matter particles have spin ½, force particles have spin 1. Each particle can spin in either direction so matter particles can be +½ or -½. What is causing these very specific values?

Spin is loosely like angular momentum and controls how particles interact and behave in a magnetic field

The comparison with angular momentum breaks down when you start measuring spin. If you were measuring angular momentum, you expect the value to depend on the axis it is measured against. For example, if something had angular momentum as shown in the blue arrow, you would expect to see a reduced spin measured around the Y axis and even less spin measured around the X axis.

After ignoring the sign of the result, measuring spin in quantum mechanics gives exactly the same values regardless of measurement axis. How can that happen?

This is where spin is NOT angular momentum. Remember that fields have a value at each point that can be a single value, a vector or something else. A more precise description of spin is:

Spin describes how a field changes when space is rotated.

Spin 0: Fields that give a single value are not affected by rotation. That is the Higgs field

Spin 1: Fields that give a vector are rotated – turning through 360˚ gets back to the original value. These are the force fields.

Spin ½: These are fields whose quantum state changes sign after a 360° rotation and returns to its original state only after a 720° rotation. These are the matter fields.

Essentially, spin is handedness of rotation, not rate of rotation! Think of a bolt thread, it is either right or left handed regardless of thread pitch or thread size.

A general quantum field is more complex than a simple wave moving in one direction. To measure spin, choose a direction and project the state onto that direction. The value of the spin is a property of the field, not the individual particles. For a photon, the result is measured as +1 or −1 regardless of the chosen axis

Polarization

The spin of photons givens them circular polarization – they either spin to the left or the right.

If photons have left or right circular polarization, how do they have the linear polarization that gets blocked by polarized sun glasses? With linear polarization, the light gets blocked by a filter depending on the direction it is oscillating. Linear polarization looks like this…

The answer brings in superposition that was discussed earlier. In the same way superposition lets a particle can have probabilities of being in different places, photon superposition gives the photon a probability of left or right spin. i.e. It has two directions available to it. Adding up the spins available in opposite directions gives the linear polarization. The phase angle between the superimposed left and right spin gives the orientation of the linear polarization